This applies to the small extra dimensions. The rolled-up compact kind that we wouldn't see if they were there. Paul Steinhardt has just posted a paper proving no-go theorems that exhibit an impressive degree of incompatibility between compact extra dimensions on the one hand versus the accelerated expansion we observe today, and also versus the widely accepted concept of early universe inflation. The extent of incompatibility is surprising, so this paper is likely to have repercussions and could arouse controversy. It appeared today. Here's the abstract: http://arxiv.org/abs/0811.1614 Dark Energy, Inflation and Extra Dimensions Paul J. Steinhardt, Daniel Wesley 26 pages, 1 figure (Submitted on 11 Nov 2008) "We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."